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fixed income analysis
Fixed Income Analysis Workbook 2nd Edition Frank J. Fabozzi - Solutions
39. Why is the debt-to-service coverage ratio used to assess the credit risk of a commercial mortgage loan?
38. With respect to a default by the borrower, how does a residential mortgage loan differ from a commercial mortgage loan?
37. Why is credit enhancement needed for a nonagency mortgage-backed security?
36. Why can’t all residential mortgage loans be securitized by either Ginnie Mae, Fannie Mae, or Freddie Mac?
35.a. An investor purchased $10 million par value of a 7% GinnieMae passthrough security agreeing to pay 102. The pool factor is 0.72. How much does the investor pay to the seller?b. Why would an investor who wants to purchase a principal-only mortgage strip not want to do so on a TBA basis?
34.a. What is a principal-only mortgage strip and an interest-only mortgage strip?b. How does an interest-only mortgage strip differ with respect to the certainty about the cash flow from a Treasury strip created from the coupon interest?c. How is the price of an interest-only mortgage strip
33.a. For a mortgage loan, is a higher or lower loan-to-value ratio an indication of greater credit risk? Explain why.b. What is the empirical relationship between defaults and loan-to-value ratio observed by studies of residential mortgage loans?
32.a. In assessing the prepayment protection offered by a seasoned PAC tranche, explain why the initial collars may provide limited insight?b. What measure provides better information about the prepayment protection offered by a seasoned PAC tranche?
31. Assume that in FJF-01 in the chapter (see Exhibit 5 in the chapter), tranche C had been split to create a floater with a principal of $80,416,667 and an inverse floater with a principal of $16,083,333.a. What would be the cap rate for the inverse floater if the coupon rate for the floater is
30. What is a broken or busted PAC?
29. An issuer is considering the following two CMO structures:Structure I:Tranche Par amount Coupon rate A $150 million 6.50%B 100 million 6.75%C 200 million 7.25%D 150 million 7.75%E 100 million 8.00%F 500 million 8.50%Tranches A-E are a sequence of PAC Is and F is the support tranche.Structure
28. Consider the following CMO structure backed by 8% collateral:Tranche Par amount Coupon rate A $400,000,000 6.25%B $200,000,000 6.75%C $225,000,000 7.50%D $175,000,000 7.75%Suppose that the structurer of this CMO wants to create a notional IO tranche with a coupon rate of 8%. Calculate the
27. Suppose that for the first four years of a CMO, prepayments are well below the initial upper PAC collar and within the initial lower PAC collar. What will happen to the effective upper collar?
26. In a CMO structure with several PAC tranches that pay off sequentially, explain what the structure effectively becomes once all the support tranches are paid off.
25. Suppose that $500 million of passthroughs are used to create a CMO structure with a PAC tranche with a par value of $350 million (PAC I), a support tranche with a schedule(PAC II) with a par value of $100 million, and a support tranche without a schedule with a par value of $200 million.a. Will
24. Suppose that the $1 billion of collateral in the CMO structure KMF-05 in the previous question was divided into a PAC tranche with a par value of $800 million and a support tranche with a par value of $200 million (instead of $650 million and $350 million). The new structure is KMF-06. Will the
23. Suppose that $1 billion of passthroughs are used to create a CMO structure, KMF-05.This structure includes a PAC tranche with a par value of $650 million and a support tranche with a par value of $350 million.a. Which of the following will have the least average life variability: (i) the
22. Suppose that a PAC bond is created using prepayment speeds of 90 PSA and 240 PSA and the average life is 5 years.Will the average life for this PAC tranche be shorter than, longer than, or equal to 5 years if the collateral pays at 140 PSA over its life? Explain your answer.
21. Suppose that the manager of a savings & loan association portfolio has decided to invest in mortgage-backed securities and is considering the following two securities: (i) a Fannie Mae passthrough security with a WAM of 310 months or (ii) a PAC tranche of a Fannie Mae CMO issue with an average
20. What is the role of a support tranche in a CMO structure?
19. EllenMorgan received a phone call from the trustee of a pension fund. Ms.Morgan is the portfolio manager for the pension fund’s bond portfolio. The trustee expressed concerns about the inclusion of CMOs in the portfolio. The trustee’s concern arose after reading several articles in the
18. ‘‘By creating a CMO, an issuer eliminates the prepayment risk associated with the underlying mortgages loans.’’ Explain why you agree or disagree with this statement?
17. How does a CMO alter the cash flow from mortgages so as to redistribute the prepayment risk across various tranches in a deal?
16. Suppose that a tranche from which a floater and an inverse floater are created has an average life of six years. What will be the average life of the floater and the inverse floater?
15. Explain why it is necessary to have a cap for the floater when a fixed-rate tranche is split into a floater and an inverse floater.
14. Suppose that in the previousCMOstructure, KMF-01, that trancheCis an accrual tranche that accrues coupon interestmonthly.Wewill refer to this newCMOstructure asKMF-02.a. What is the principal repayment, interest, and cash flow for tranche A in KMF-02?b. What is the principal balance for tranche
13. Suppose that a portfolio manager is considering a collateralized mortgage obligation structure KMF-01. This structure has three tranches. The deal is a simple sequential pay and was issued several years ago. The tranches are A, B, and C with a coupon rate paid to each tranche each month and
12. What type of prepayment risk is an investor interested in a short-term security concerned with when purchasing a mortgage-backed security?
11. Suppose that you are analyzing prepayments of a passthrough security that was issued more than 15 years ago. The weighted average coupon (WAC) for the underlying mortgage pool was 13%. Suppose that the mortgage rate over the year of the analysis declined from 8% to 7% but prepayments for this
10. Robert Reed is an assistant portfolio managerwho has been recently given the responsibility of assisting Joan Soprano, the portfolio manager for the mortgage-backed securities portfolio. Ms. Soprano gave Mr. Reed a copy of the a Prudential Securities publication for November 1999 entitled
9. Comment on the following statement: ‘‘The PSA model is a prepayment model.’’
8. Suppose that in month 140 the mortgage balance for a mortgage pool underlying a passthrough security is $537 million and that the scheduled principal repayment for month 140 is $440,000. Assuming 175 PSA, what is the amount of the prepayment for month 140?
7. Explain why 30 months after the origination of a mortgage pool, discussing prepayments in terms of one CPR and a PSA are identical.
6. Using the Public Securities Association Prepayment benchmark, complete the following table:Month PSA CPR SMM 5 100 15 80 20 175 27 50 88 200 136 75 220 225
5. Mr. Jamison is looking at the historical prepayment for a passthrough security. He finds the following:mortgage balance in month 42 = $260,000,000 scheduled principal payment in month 42 = $1,000,000 prepayment in month 42 = $2,450,000a. What is the SMM for month 42?b. How should Mr. Jamison
4. Consider the following mortgage pool.Loan Outstanding mortgage balance Mortgage rate Months remaining 1 $215,000 6.75% 200 2 $185,000 7.75% 185 3 $125,000 7.25% 192 4 $100,000 7.00% 210 5 $200,000 6.50% 180 Total $825,000a. What is the weighted average coupon rate for this mortgage pool?b. What
3. Explain why you agree or disagree with the following statement: ‘‘Since mortgage passthrough securities issued by Ginnie Mae are guaranteed by the full faith and credit of the U.S. government, there is no uncertainty about the cash flow for the security.’’
2.a. Suppose that the servicing fee for a mortgage loan is 0.5%. Complete the following schedule for the mortgage loan in the previous question. The column labeled ‘‘Servicing Fee’’ is the dollar amount of the servicing fee for the month. The column labeled ‘‘Net Interest’’ is the
1.a. Complete the following schedule for a 30-year fully amortizing mortgage loan with a mortgage rate of 7.25% where the amount borrowed is $150,000. The monthly mortgage payment is $1,023.26.Beginning Mortgage Sch. Prin End of month Month mortgage payment Interest repayment balance 1 150,000.00
• explain the features of a commercial mortgage loan and provisions for protecting the lender against prepayment risk.
• differentiate credit risk analysis of commercial mortgage-backed securities from residential nonagency mortgage-backed securities.
• compare and contrast agency and nonagency mortgage-backed securities.
• explain the investment characteristics of principal-only and interest-only mortgage strips.
• distinguish among sequential-pay tranche, accrual tranche, planned amortization class tranche, and support tranche in a CMO with respect to the risk characteristics and the relative performance of each, given changes in prepayment rates due to changes in interest rates.
• explain why and how a collateralized mortgage obligation is created and how a CMO distributes prepayment risk among tranches so as to create products that provide a better matching of assets and liabilities for institutional investors.
• explain contraction and extension prepayment risks and why they occur.
• discuss the factors that affect prepayments.
• explain why the average life of a mortgage-backed security is a more relevant measure than the security’s legal maturity.
• compare and contrast the single monthly mortality rate, conditional prepayment, and the Public Securities Association (PSA) prepayment benchmark that are used to set assumed prepayment rates, including their relationship to each other.
• explain the importance of prepayments to the estimation of the cash flow of a mortgagebacked security.
• describe prepayments and how they result in prepayment risk.
• describe a mortgage loan and explain the cash flow characteristics of a fixed-rate, level payment, fully amortized mortgage loan.
26.a. The valuation of a convertible bond using an options approach requires a two-factor model. What is meant by a two-factor model and what are the factors?b. In practice, is a two-factor model used to value a convertible bond?
25. Explain the limitation of using premium over straight value as a measure of the downside risk of a convertible bond?
24. The following excerpt is taken from an article entitled ‘‘Caywood Looks for Convertibles,’’that appeared in the January 13, 1992 issue of BondWeek, p. 7:Caywood Christian Capital Management will invest new money in its $400 million high-yield portfolio in ‘‘busted
23. Suppose that the price of the common stock declines from $25 to $10.a. What will be the approximate return realized from investing in the convertible bond if an investor had purchased the convertible for $900 and the straight value does not change?b. What would be the return realized if $25 had
22. Suppose that the price of the common stock of Miser Electronics whose convertible bond was described in the previous question increases from $25 to $54.a. What will be the approximate return realized from investing in the convertible bond if an investor had purchased the convertible for $900?b.
21. Consider the convertible bond by Miser Electronics:par value = $1, 000 coupon rate = 8.5%market price of convertible bond = $900 conversion ratio = 30 estimated straight value of bond = $700 Assume that the price of Miser Electronics common stock is $25 and that the dividend per share is $1 per
20. In theOctober 26, 1992 prospectus summary of The Staples 5% convertible subordinated debentures due 1999 the offering stated: ‘‘Convertible into Common Stock at a conversion price of $45 per share . . . ’’ Since the par value is $1,000, what is the conversion ratio?
19.a. In what sense does a convertible bond typically have multiple embedded options?b. Why is it complicated to value a convertible bond?
18. In valuing a floating rate note, it is necessary to make a modification to the backward induction method.a. Why is the adjustment necessary?b. What adjustment is made?c. If the floating rate note has a cap, how is that handled by the backward induction method?
17. Suppose that a callable bond has an option-adjusted spread of zero. Does that mean the corporate bond is being overvalued in the market (i.e., trading rich)?
16. Suppose that a callable bond is valued using as the benchmark interest rates the on-the-run yield curve of the issuer and that the yield for the 10-year issue is 6%. Suppose further that the option-adjusted spread computed for a 10-year callable bond of this issuer is 20 basis points. Is it
15. Four portfolio managers are discussing the meaning of option-adjusted spread. Here is what each asserted:Manager 1: ‘‘The option-adjusted spread is a measure of the value of the option embedded in the bond. That is, it is the compensation for accepting option risk.’’Manager 2: ‘‘The
14. In computing the effective duration and convexity of a bond with an embedded option, what assumption is made about the option-adjusted spread when rates change?
13. An assistant portfolio manager is trying to find the duration of a callable bond of FeedCo Corp. One vendor of analytical systems reported that the duration for the issue is 5.4. A dealer firm reported that the duration is 4.5. The assistant portfolio manager was confused by the difference in
12. Explain why, when the binomial model is used to obtain the values to be used in the formula for computing duration and convexity, the measures computed are an effective duration and effective convexity.
11. An assistant portfolio manager described the process for valuing a bond that is both callable and putable using the binomial model as follows:‘‘The process begins by first valuing one of the embedded options, say the call option. Then the model is used to value the put option. The value of
10.a. Explain why the greater the assumed interest rate volatility the lower the value of a callable bond?b. Explain why the greater the assumed interest rate volatility the higher the value of a putable bond?
9. In explaining the option-adjusted spread to a client, a manager stated the following: ‘‘The option-adjusted spread measures the yield spread using the Treasury on-the-run yield curve as benchmark interest rates.’’ Comment on this statement.
8. The manager of an emerging market bond portfolio is approached by a broker about purchasing a new corporate bond issue in Brazil. The issue is callable and the broker’s firm estimates that the option-adjusted spread is 220 basis points. What questions would you ask the broker with respect to
7. A portfolio manager must mark a bond position to market. One issue, a callable issue, has not traded in the market recently. So to obtain a price that can be used to mark a position to market, the manager requested a bid from a dealer and a value from a pricing service.The dealer bid’s price
6. In discussing the approach taken by its investment management firm in valuing bonds, a representative of the firm made the following statement:‘‘Our managers avoid the use of valuation methodologies such as the binomial model or other fancier models because of the many assumptions required
5. The on-the-run issue for the Inc.Net Company is shown below:Maturity (years) Yield to maturity (%) Market price 1 7.5 100 2 7.6 100 3 7.7 100 Using the bootstrapping methodology, the spot rates are:Maturity (years) Spot rate (%)1 7.500 2 7.604 3 7.710 Assuming an interest rate volatility of 10%
4.a. When valuing an option-free bond, short-term forward rates can be used. When valuing a bond with an embedded option, there is not one forward rate for a period but a set of forward rates for a given period. Explain why.b. Explain why the set of forward rates for a given period depend on the
3. Why is the value produced by a binomial model and any similar models referred to as an‘‘arbitrage-free value’’?
2. Why is the procedure for valuing a bond with an embedded option called ‘‘backward induction’’?
1. Comment on the following statement:‘‘There are several arbitrage-free models for valuing callable bonds. Thesemodels differ significantly in terms of how interest rates may change in the next period.There are models that allow the rate in the next period to take on only one of two values.
• compare the risk/return characteristics of a convertible bond’s value to the risk/return characteristics of the underlying common stock.
• discuss the components of a convertible bond’s value that must be included in an option-based valuation approach.
• compute and explain the meaning of the following for a convertible bond: conversion value, straight value, market conversion price, market conversion premium per share, market conversion premium ratio, premium payback period, and premium over straight value.
• describe the basic features of a convertible bond.
• compute the value of a putable bond using the binomial model.
• calculate effective duration and effective convexity using the binomial model.
• calculate an option-adjusted spread using the binomial model and interpret an optionadjusted spread with respect to the benchmark interest rates.
• explain the effect of volatility on the arbitrage-free value of a bond with an embedded option.
• explain the relationship among the values of a bond with an embedded option, the corresponding option-free bond, and the embedded option.
• explain how the value of an embedded option is determined.
• compute the value of a callable bond from an interest rate tree given the call schedule and the rule for calling a bond.
• explain the backward induction valuation methodology within the binomial interest rate tree framework.
• explain the binomial interest rate modeling strategy.
• explain the importance of the benchmark interest rates in interpreting spread measures.
23.a. In forecasting yield volatility, why would a manager not want to weight each daily yield change equally?b. In forecasting yield volatility, what is recommended for the sample mean in the formula for the variance or standard deviation?
22.a. What is implied volatility?b. What are the problems associated with using implied volatility as a measure of yield volatility?
21. Suppose that the annualized standard deviation of the 2-year Treasury yield based on daily yields is 7% and the current level of the 2-year Treasury yield is 5%. Assuming that the probability distribution for the percentage change in 2-year Treasury yields is approximately normally distributed,
20. Comment on the following statement: ‘‘Two portfolio managers with the same set of daily yields will compute the same historical annual volatility.’’
19. For the daily yield volatility computed in the previous question, what is the annual yield volatility assuming the following number of days in the year:(a) 250 days?(b) 260 days?(c) 365 days?
18. Compute the 10-day daily standard deviation of the percentage change in yield assuming continuous compounding assuming the following daily yields.t yt 0 5.854 1 5.843 2 5.774 3 5.719 4 5.726 5 5.761 6 5.797 7 5.720 8 5.755 9 5.787 10 5.759
17. Below are the key rate durations for three portfolios of U.S. Treasury securities all with the same duration for a parallel shift in the yield curve.(a) For each portfolio describe the type of portfolio (barbell, ladder, or bullet).Key rate maturity Portfolio A Portfolio B Portfolio C 3-month
16. You are the financial consultant to a pension fund. After your presentation to the trustees of the fund, you asked the trustees if they have any questions. You receive the two questions below. Answer each one.a. ‘‘The yield curve is upward-sloping today. Doesn’t this suggest that the
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